What will I learn today? Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

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What will I learn today? Learn to understand ratios and proportions in scale drawings. Learn to use ratios and proportions with scale.

This HO gauge model train is a scale model of a historic train This HO gauge model train is a scale model of a historic train. A scale model is a proportional model of a three-dimensional object. Its dimensions are related to the dimensions of the actual object by a ratio called the scale factor. The scale factor of an HO gauge model train is . 1 87 This means that each dimension of the model is of the corresponding dimension of the actual train. 1 87

A scale is the ratio between two sets of measurements A scale is the ratio between two sets of measurements. Scales can use the same units or different units. The photograph shows a scale drawing of the model train. A scale drawing is a proportional drawing of an object. Scale drawings and scale models can be smaller or larger than the objects they represent.

Steps to finding scale factor: S1: Write a ratio with the model’s dimensions over the actual object’s dimensions. S2: Reduce the ratio to the simplest form.

Example 1: Finding a Scale Factor Identify the scale factor. Room Blueprint Length (in.) 144 18 Width (in.) 108 13.5 blueprint length room length 18 144 Write a ratio using one of the dimensions. = 1 8 = Simplify. 1 8 The scale factor is .

Insert Lesson Title Here Example 2 Identify the scale factor. Model Aircraft Blueprint Length (in.) 12 2 Wing span (in.) 18 3 blueprint length aircraft length 2 12 Write a ratio using one of the dimensions. = 1 6 = Simplify.

Example 3: On a road map, the distance between Pittsburgh and Philadelphia is 7.5 inches. What is the actual distance between the cities if the map scale is 1.5 inches = 60 miles? Let d be the actual distance between the cities. 1.5 60 = 7.5 d Write a proportion. Find the cross products. 1.5d = 450 450 1.5 1.5d 1.5 = Divide both sides by 1.5. d = 300 The distance between the cities is 300 miles.

Lesson Quiz: Part I Identify the scale factor. Statue of Liberty Model Height (in.) 1,824 8 1. 1 228 On a scale drawing, a kitchen wall is 6 inches long. The scale factor is . What is the length of the actual wall? 1 24 2. 144 inches, or 12 feet

Insert Lesson Title Here Lesson Quiz: Part II 3. On a road map, the distance from Green Bay to Chicago is 11 cm. What is the actual distance between the cities if the map scale is 3 cm = 90 km? 330 km